To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .

To send content items to your Kindle, first ensure no-reply@cambridge.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

By using this service, you agree that you will only keep articles for personal use, and will not openly distribute them via Dropbox, Google Drive or other file sharing services
Please confirm that you accept the terms of use.

The following paper contains a purely analytical discussion of the problem of the deformation of an isotropic elastic plate under given forces. The problem is an unusually interesting one. It was the first to be attacked (by Lamé and Clapeyron in 1828) after the establishment of the general equations by Navier. The solution of the problem of normal traction given by these authors, when reduced to its simplest form, involves double integrals of simple harmonic functions of the coordinates. The integrals are of complicated form, and practically impossible to interpret, a fact which, without doubt, has had much to do with the neglect of the problem in later times, and the almost complete absence of attempts to establish the approximate theory on the basis of an exact solution. An even more serious defect of Lamé and Clapeyron's solution is that the integrals, as they stand, do not converge. A flaw of this sort has often been treated lightly by physical writers, the non-convergence of an integral being regarded as due to the inclusion of an infinite but unimportant constant. In the present case, however, the infinite terms are not constant, but functions of the coordinates, and the modifications necessary to secure convergence, so far from being unimportant, lead directly to the most significant terms of the solution.

This chapter provides an overview of the legislative frameworks that are relevant to the management of violence by persons with mental disorders in the UK. As three jurisdictions apply (England and Wales, Scotland, and Northern Ireland), individual frameworks and their variants are not discussed in detail. Rather, substantial differences relevant to the management of violence are highlighted. Professionals should refer to the respective frameworks for detailed guidance.

Management of violence refers not only to acute episodes, but also to the prevention or reduction of the risk of future violence. The core principles guiding routine medical practice of ‘consent’ and ‘do no harm’ remain relevant. Legislation provides a framework when coercion may be necessary to manage an acute violent act, manage the immediate risk of further violence or manage longer-term risk of violence.

Three strands of legislation are relevant to this report: the Human Rights Act 1998, mental health acts and mental capacity acts. The Human Rights Act applies to all three jurisdictions. The Mental Capacity Act 2005 and the Mental Health Act 1983 apply to England and Wales. Scotland is covered by the Mental Health (Care and Treatment) (Scotland) Act 2003 and the Adults with Incapacity (Scotland) Act 2000. Mental health legislation in Northern Ireland comprises the Mental Health (Amendment) (Northern Ireland) Order 2004. In certain circumstances, common law ‘duty of care’ may also be relied on, which remains necessary in Northern Ireland and which does not yet have an equivalent to the Mental Capacity Act.

Human Rights Act 1998

Compliance with the Human Rights Act is required when a function is of a public nature. The Act requires public authorities to act in accordance with the European Convention on Human Rights and the European Court of Human Rights (ECHR) which came into force in 1953. The Act would, for example, apply to the NHS and local authorities. It recognises certain rights and freedoms, with the ECHR hearing alleged breaches. The Act serves to allow UK citizens to seek redress in the UK regarding possible contraventions without having to apply immediately to the ECHR.

The theory of representations of finite simple groups of Lie type in defining characteristic is somewhat advanced. The representations arise from those of the associated algebraic groups, and so some familiarity with the theory of algebraic groups is necessary in order to understand it. For an introduction to this theory see, for example, the survey article by Humphreys [51]. The enthusiastic reader may wish to consult Jantzen [58] for a more detailed exposition. Humphrey's classic book [50] provide a general exposition of the theory of algebraic groups and their representations, whilst Malle and Testerman's book [91] gives an excellent introduction to the general theory, subgroup structure, and representation theory of the finite and algebraic groups of Lie type, including a fuller discussion of all of the introductory material in this chapter.

In many respects, the study of the J2-candidates is easier than that of the J1-candidates, simply because there are far fewer of them: we just need to know about the representations in dimensions up to 12, and to be able to determine some of their properties, such as forms preserved and their behaviour under the actions of group and field automorphisms. Fortunately it is possible to extract this information starting from a superficial familiarity with the main results of the theory, principally the Steinberg Tensor Product Theorems. These theorems, together with the tables in [84], suffice to determine the representations.

This book classifies the maximal subgroups of the almost simple finite classical groups in dimension up to 12; it also describes the maximal subgroups of the almost simple finite exceptional groups with socle one of Sz(q), G2(q), 2G2(q) or 3D4(q). Theoretical and computational tools are used throughout, with downloadable Magma code provided. The exposition contains a wealth of information on the structure and action of the geometric subgroups of classical groups, but the reader will also encounter methods for analysing the structure and maximality of almost simple subgroups of almost simple groups. Additionally, this book contains detailed information on using Magma to calculate with representations over number fields and finite fields. Featured within are previously unseen results and over 80 tables describing the maximal subgroups, making this volume an essential reference for researchers. It also functions as a graduate-level textbook on finite simple groups, computational group theory and representation theory.

The main purpose of the following investigation is to improve the existing Approximate Theory of Beams by bringing it into closer relationship than has hitherto been done with exact solutions of the fundamental differential equations of equilibrium. In its aim, method, and results the paper closely resembles one already published in these Transactions on the corresponding Theory for Plates (vol. xli., 1904). It is less comprehensive than the latter paper, as it deals only with a beam of circular section; but the analysis is of such a nature that the chief results can be extended almost immediately to a beam of any form of section, on the assumption merely of certain Existence Theorems.

This study provides an empirical test of North and Weingast's theory of British capital-market development after the Glorious Revolution. The evidence is consistent with the hypotheses that institutional innovation in the 1690s led to the dramatic growth in London capital markets, and that threats to these institutions caused financial turmoil. We also find the economic motivation for these innovations to be consistent with the work of Ekelund and Tollison.

1. It is known that any polynomial in μ. can be expanded as a linear function of Legendre polynomials [1]. In particular, we have

The earlier coefficients, say A0, A2, A4 may easily be found by equating the coefficients of μp+q, μp+q-2, μp+q-4 on the two sides of (1). The general coefficient A2k might then be surmised, and the value verified by induction. This may have been the method followed by Ferrers, who stated the result as an exercise in his Spherical Harmonics (1877). A proof was published by J. C. Adams [2]. The proof now to be given follows different lines from his.

The object of the present paper is to establish the equivalence of the well-known theorem of the double-six of lines in projective space of three dimensions and a certain theorem in Euclidean plane geometry. The latter theorem is of considerable interest in itself for two reasons. In the first place, it is a natural extension of Euler's classical theorem connecting the radii of the circumscribed and the inscribed (or the escribed) circles of a triangle with the distance between their centres. Secondly, it gives in a geometrical form the invariant relation between the circle circumscribed to a triangle and a conic inscribed in the triangle. For a statement of the theorem, see § 13 (4).